Whidborne, James F.McKernan, JohnPapadakis, George2011-09-292011-09-292008-01-01J F Whidborne, J McKernan, G Papadakis; Minimizing transient energy growth in plane Poiseuille flow. Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, Special issue on Flow Control, 2008, Volume 222, Number 5 / 323-3310959-6518http://dx.doi.org/10.1243/09596518JSCE493http://dspace.lib.cranfield.ac.uk/handle/1826/3339The feedback control of laminar plane Poiseuille flow is considered. In common with many flows, the dynamics of plane Poiseuille flow is very non-normal. Consequently, small perturbations grow rapidly with a large transient that may trigger non-linearities and lead to turbulence, even though such perturbations would, in a linear flow, eventually decay. This sensitivity can be measured using the maximum transient energy growth. The linearized flow equations are discretized using spectral methods and then considered at one wave-number pair in order to obtain a model of the flow dynamics in a form suitable for advanced control design. State feedback controllers that minimize an upper bound on the maximum transient energy growth are obtained by the repeated solution of a set of linear matrix inequalities. The controllers are tested using a full Navier–Stokes solver, and the transient energy response magnitudes are significantly reduced compared with the uncontrolled casen-UKflow controltransient energy growthlinear matrix inequality (LMI)Navier–Stokesplane Poiseuille flowArticle